Higgs boson, renormalization group, and naturalness in cosmology (0910.1041v3)

Abstract: We consider the renormalization group improvement in the theory of the Standard Model (SM) Higgs boson playing the role of an inflaton with a strong non-minimal coupling to gravity. At the one-loop level with the running of constants taken into account, it leads to a range of the Higgs mass that is entirely determined by the lower WMAP bound on the cosmic microwave background (CMB) spectral index. We find that the SM phenomenology is sensitive to current cosmological data, which suggests to perform more precise CMB measurements as a SM test complementary to the LHC program. By using the concept of a field-dependent cutoff, we show the naturalness of the gradient and curvature expansion in this model within the conventional perturbation theory range of the SM. We also discuss the relation of these results to two-loop calculations and the limitations of the latter caused by parametrization and gauge dependence problems.

• The paper demonstrates that renormalization group improvements yield a constrained Higgs mass range consistent with precise CMB data.
• The study employs one-loop running constants and a strong non-minimal coupling to refine predictions of the Higgs inflation model.
• It highlights a synergy between particle physics and cosmology, suggesting future tests with improved two-loop analyses to address gauge dependence.

Higgs Boson, Renormalization Group, and Naturalness in Cosmology

The paper "Higgs boson, renormalization group, and naturalness in cosmology" meticulously investigates the integration of the Higgs boson within cosmological models, specifically focusing on its role as an inflaton in the early universe. The authors explore the ramifications of a strong non-minimal coupling to gravity and utilize renormalization group improvements to refine the theoretical predictions of the Higgs inflation model.

Overview of the Study

The researchers delve into the Standard Model (SM) extended to account for Higgs inflation, where the Higgs field serves as an inflaton—a scalar field responsible for driving inflation. The paper emphasizes the importance of renormalization group improvements, incorporating one-loop level calculations with running constants, thereby resulting in a Higgs mass range constrained by cosmic microwave background (CMB) data, notably the spectral index.

A significant claim of the paper is that SM phenomena are notably sensitive to current cosmological observations, suggesting a synergy between more precise CMB measurements and the LHC program for testing SM predictions. The paper critically examines the conventional perturbation theory and its limitations, especially concerning gauge dependence, and hints at the necessity for viable two-loop calculations in fully capturing the dynamics of Higgs inflation.

Key Numerical Results and Claims

• Higgs Mass Range: The researchers derive a Higgs mass range consistent with existing CMB data, establishing lower limits exceeding prior expectations from collider experiments. This result underscores the influence of renormalization group improvements, particularly the running of SM coupling constants.
• Parameter Sensitivity: The inflationary anomalous scaling, denoted as $\mathbf{A_I}$, emerges as a crucial parameter in determining the CMB-compatible range of the Higgs mass, transforming across scales due to renormalization group dynamics.

Implications and Speculations on Future Developments

The findings propose significant implications for the interplay between particle physics and cosmology, especially highlighting the potential of cosmological observations to inform SM physics. The interplay between Higgs inflation and CMB measurements might offer critical tests for theoretical physics, potentially refining or challenging existing models.

In terms of theoretical advancements, the paper suggests the necessity of resolving gauge dependence issues and developing robust methodologies for gauge and parametrization-independent cosmological observables. As new data surfaces, this research paves the way for a more integrated understanding of cosmological evolution and its linkage to fundamental particle physics.

Final Thoughts

The paper articulates the alignment between Higgs inflation theory and observational cosmology, providing a comprehensive analysis of the theoretical implications of integrating SM phenomena in cosmological models. While the paper reinforces the viability of this model, it also delineates numerous uncertainties and technical challenges, indicating fertile ground for further inquiry. The exploration of Higgs inflation is positioned as an essential conduit for elucidating the origins and dynamics of the universe, inviting future research to navigate and expand upon these complex intersections of physics.